Synthesis and Swelling Behavior of pH-Responsive Polybase Brushes

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Langmuir 2007, 23, 5769-5778

5769

Synthesis and Swelling Behavior of pH-Responsive Polybase Brushes S. Sanjuan, P. Perrin, N. Pantoustier, and Y. Tran* Laboratoire de Physico-chimie des Polyme` res et des Milieux Disperse´ s, ESPCI, CNRS, UPMC, 10, rue Vauquelin. 75231 Paris Cedex 05, France ReceiVed NoVember 27, 2006. In Final Form: February 21, 2007 We synthesize polybase brushes and investigate their swelling behavior. Poly(2-(dimethylamino)ethyl methacrylate)) (PDMAEMA) brushes are prepared by the “grafting from” method using surface-initiated Atom Transfer Radical Polymerization to obtain dense brushes with relatively monodisperse chains (PDI ) 1.35). In situ quaternization reaction can be performed to obtain poly(2-(trimethylamino)ethyl methacrylate)) (PTMAEMA) brushes. We determine the swollen thickness of the brushes using ellipsometry and neutron reflectivity techniques. Brushes are submitted to different solvent conditions to be investigated as neutral brushes and weak and strong polyelectrolyte brushes. The swelling of the brushes is systematically compared to scaling models. It should be pointed out that the scaling analysis of different types of brushes (neutral polymer and weak and strong polyelectrolyte brushes) is performed with identical samples. The scaling behavior of the PDMAEMA brush in methanol and the PTMAEMA brush in water is in good agreement with the predicted scaling laws for a neutral polymer brush in a good solvent and a polyelectrolyte brush in the osmotic regime. The salt-induced contraction of the quaternized brush is observed for high salt concentration, in agreement with the predicted transition between the regimes of the osmotic brush and the salted brush. From the crossover concentration, we calculate the effective charge ratio of the brush following the Manning counterion condensation. We also use PDMAEMA brushes as pH-responsive polybase brushes. The swelling behavior of the polybase brush is intermediate with respect to the behavior of the neutral polymer brush in a good solvent and the behavior of the quenched polyelectrolyte brush, as expected. The effective charge ratio of the PDMAEMA brush is determined as a function of pH using the scaling law of the polyelectrolyte brush in the osmotic regime.

Introduction Polymer brushes made of polymer chains densely attached to a surface are of great interest in a wide field of industrial and biological applications as well as in academic research. Polymer brushes are extensively used for the improvement of adhesion, lubrication, tribology, wetting properties, and colloidal stabilization. More recently, some strategies have been developed for the functionalization of surfaces with polymer brushes to realize smart surfaces with switchable-adaptative-responsive properties and to generate micropatterned polymer monolayers.1-3 Responsive polymer brushes are attractive owing to the change in the conformation of attached chains according to external conditions. For example, neutral polymer chains are sensitive to solvent quality. For polyelectrolyte chains, the influence of the environment on their charge is crucial. An important distinction has to be made regarding “strong” and “weak” polyelectrolytes. For strong (also called “quenched”) polyelectrolyte brush, the number and position of the charges on the chain are fixed because charges are permanently associated with a chemical group. Weak (or “annealed”) polyelectrolyte brushes are pH-dependent with a dissociation-association equilibrium governing the average degree of charge. Weak polyacids and polybases are thus used as pH-responsive brushes. There are many ways to force polyelectrolyte chains into brushlike systems. The conditions required are that the chains are connected irreversibly to the surface of the substrate and the * To whom all correspondence should be addressed. E-mail: [email protected]. Phone: 33 1 40 79 58 12. Fax: 33 1 40 79 46 40. (1) Advincula, R. C., Brittain, W. J., Caster, K. C., Ru¨he, J., Eds. Polymer Brushes; Wiley-VCH: Weinheim, Germany, 2004. (2) Ru¨he, J.; Ballauff, M.; Biesalski, M.; Dziezok, P.; Gro¨hn, F.; Johannsmann, D.; Houbenov, N.; Hugenberg, N.; Konradi, R.; Minko, S.; Motornov, M.; Netz, R.; Schmidt, M.; Seidel, C.; Stamm, M.; Stephan, T.; Usov, D.; Zhang, H. AdV. Polym. Sci. 2004, 165, 79. (3) Zhao, B.; Brittain, W. J. Progr. Polym. Sci. 2000, 25, 677.

distance between anchoring points is small enough to induce significant chains stretching. Brushlike systems could be obtained from amphiphilic block copolymers spread at the air-water interface or adsorbed on a solid substrate. Polymer brushes in which the chains are covalently bound to the surface of a solid substrate are probably the most difficult to prepare. Historically, the first covalently surface-attached polyelectrolyte chains were synthesized by the “grafting to” strategy where preformed chains containing appropriate end-functionalized groups are reacted with the surface to obtain the desired brush. Chains with chlorosilane termination were anchored to silicon wafer substrates by the reaction of chlorosilane with the hydroxyl surface functionality.4-6 A two-step process was also developed: the glycidoxypropyl trimethoxysilane was first grafted to a silicon wafer and carboxylterminated chains were then anchored to the modified silica surface.7,8 These methods allow the grafting of neutral polymer chains. For polyelectrolyte brushes, an additional step was necessary for the conversion of neutral polymer to polyelectrolyte. In the more recent “grafting from” technique, the polymer is formed directly at the surface of the substrate by using a monolayer of surface-attached initiators to perform a surface-initiated polymerization reaction. In general, the grafting from method allows the formation of polymer brushes that are denser than that obtained using the grafting to technique. An explanation would be that, in the grafting from approach, monomer units (and not the whole polymer chain) migrate to the growing polymer brush layer. An increasing number of polymerization techniques using appropriate initiators previously attached to the surface is currently being developed. They include ring-opening, ring-opening (4) Mir, Y.; Auroy, P.; Auvray, L. Phys. ReV. Lett. 1995, 75, 2863. (5) Tran, Y.; Auroy, P.; Lee, L. T. Macromolecules 1999, 32, 8952. (6) Tran, Y.; Auroy, P. J. Am. Chem. Soc. 2001, 123, 3644. (7) Minko, S.; Pati, S.; Datsyuk, V.; Simon, F.; Eichhorn, K. J.; Motornov, M.; Usov, D.; Tokarev, I.; Stamm, M. Langmuir 2002, 18, 289. (8) Luzinov, I.; Julthongpiput, D.; Malz, H.; Pionteck, J.; Tsukruk, V. V. Macromolecules 2000, 33, 1043.

10.1021/la063450z CCC: $37.00 © 2007 American Chemical Society Published on Web 04/11/2007

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metathesis, or anionic polymerizations and also controlled radical polymerizations, which allow the polymerization of a larger range of monomers. For instance, RAFT (reversible addition fragmentation transfer), NMP (nitroxide-mediated polymerization), and ATRP (Atom Transfer Radical Polymerization)9,10 have actually been performed to synthesize poly(acrylate)- and poly(styrene)-based polymer brushes.11-19 From a theoretical viewpoint, the structure of strong and weak polyelectrolyte brushes was investigated in many key papers.20-30 Historically, the scaling behavior of neutral polymer brushes was first described by Alexander31 and De Gennes.32,33 Theoretical studies on polyelectrolyte brushes emerged in the early 1990s with Pincus,20 and Borisov and co-authors.21,22 The swollen thickness L of neutral polymer brushes in a good solvent is given by

L ∝ Na5/3σ1/3

(1)

with a being the monomer size, σ being the grafting density, which is defined as the number of chains per unit area, and N being the chain length (N is the number of monomers per chain or the degree of polymerization). This scaling relation is obtained from the balance between the osmotic pressure of the monomers that tends to stretch the chains and the restoring elastic forces. For polyelectrolyte brushes, the chain conformation is governed by the electrostatic interactions between the charged monomers and the osmotic pressure of the counterions. Different regimes exist depending on the chain length, the grafting density, the charge fraction, and the ionic strength of the solution. The “osmotic regime” is predicted for sufficiently dense and strongly charged brushes. In this regime, all counterions are confined inside the brush to compensate for the charges associated with surface-attached chains, and the brush (9) Xia, J.; Matyjaszewski, K. Chem. ReV. 2001, 101, 2921. (10) Patten, T. E.; Matyjaszewski, K. AdV. Mater. 1998, 10, 901. (11) Husseman, M.; Malmstro¨m, E. E.; McNamara, M.; Mate, M.; Mecerreyes, D.; Benoit, D. G.; Hedrick, J. L.; Mansky, P.; Huang, A.; Russell, T.; Hawker, C. J. Macromolecules 1999, 32, 1424. (12) Matyjaszewski, K.; Miller, P. J.; Shukla, N.; Immaraporn, B.; Gelman, A.; Luokola, B. B.; Siclovan, T. M.; Kickelbick, G. Vallant, T.; Hoffmann, H.; Pakula, T. Macromolecules 1999, 32, 8716. (13) Zhao, B.; Brittain, W. J. Macromolecules 2000, 33, 8813. (14) Ejaz, M.; Ohno, K.; Tsujii, Y.; Fukuda, T. Macromolecules 2000, 33, 2870. (15) Kong, X.; Kawai, T.; Abe, J.; Iyoda, T. Macromolecules 2001, 34, 1837. (16) Boyes, S. G.; Brittain, W. J.; Weng, X.; Cheng, S. Z. D. Macromolecules 2002, 35, 4960. Boyes, S. G.; Akgun, B.; Brittain, W. J.; Foster, M. D. Macromolecules 2003, 36, 9539. (17) Sankhe, A. Y.; Husson, S. M.; Kilbey, S. M., II Macromolecules 2006, 39, 1376. (18) Topham, P. D.; Howse, J. R.; Crook, C. J.; Parnell, A. J.; Geoghegan, M.; Jones, R. A. L.; Ryan, A. J. Polym. Int. 2006, 55, 808. (19) Ryan, A. J.; Crook, C. J.; Howse, J. R.; Topham, P.; Jones, R. A. L.; Geoghegan, M.; Parnell, A. J.; Ruiz-Pe´rez, L.; Martin, S. J.; Cadby, A.; Menelle, A.; Webster, J. R. P.; Gleeson, A. J.; Bras, W. Faraday Discuss. 2005, 128, 55. (20) Pincus, P. Macromolecules 1991, 24, 2912. (21) Borisov, O. V.; Birshtein, T. M.; Zhulina, E. B. J. Phys. II (Paris) 1991, 1, 521. (22) Zhulina, E. B.; Borisov, O. V.; Birshtein, T. M. J. Phys. II (Paris) 1992, 2, 63. (23) Ross, R. S.; Pincus, P. Macromolecules 1992, 25, 2177. (24) Wittmer, J.; Joanny, J. F. Macromolecules 1993, 26, 2691. (25) Israe¨ls, R.; Leermakers, F. A. M.; Fleer, G. J. Macromolecules 1994, 27, 3087. (26) Israe¨ls, R.; Leermakers, F. A. M.; Fleer, G. J.; Zhulina, E. B. Macromolecules 1994, 27, 3249. (27) Borisov, O. V.; Zhulina, E. B.; Birshtein, T. M. Macromolecules 1994, 27, 4795. (28) Zhulina, E. B.; Birshtein, T. M.; Borisov, O. V. Macromolecules 1995, 28, 1491. (29) Zhulina, E. B.; Borisov, O. V. J. Chem. Phys. 1997, 107, 5952. (30) Borisov, O. V.; Zhulina, E. B. J. Phys. II France 1997, 7, 449. (31) Alexander, S. J. Phys. (Paris) 1977, 28, 977. (32) de Gennes, P. G. J. Phys. (Paris) 1976, 37, 1445. (33) de Gennes, P. G. Macromolecules 1980, 13, 1069.

height is independent of the grafting density. It is a function only of the chain length N and the effective charge ratio f

L ∝ Naf1/2

(2)

At low added salt concentrations, the screening disturbs only the outer edge of the brush, leaving the brush height unchanged. Once the added salt concentration cS reaches the concentration of the free counterions inside the brush, the polyelectrolyte layer is more contracted and the brush height is given by

L ∝ Na2/3σ1/3f2/3cS-1/3

(3)

It should be noted that in this “salted brush” regime the scaling law is the same as for a neutral polymer brush with an electrostatic excluded volume. In weak polyelectrolyte brushes, the degree of dissociation is decisive for chains stretching. Also, the number of added salt ions has to be compared to the number of free counterions. Weak polyelectrolyte brushes behave as quenched brushes for high added salt concentrations, but when the number of added salt ions is not in large excess, they can modify the degree of dissociation inside the brush by the exchange between the added cations and the protons. As a consequence, the addition of salt leads to a larger fraction of dissociated monomer units, resulting in an increase in the osmotic pressure. In this annealed osmotic brush regime, the brush height is given by

L ∝ Na4/3σ-1/3

[( )

]

fb (c + cS) 1 - f b H+

1/3

(4)

where fb is the degree of dissociation of a single chain in the bulk solution and cH+ is the concentration of protons in the solution. Surprisingly, only a few experimental investigations on the structure of polyelectrolyte brushes are in good agreement with the scaling laws predicted by mean-field theories. Let us mention the studies of Biesalski and Ru¨he on poly(4-vinyl pyridine) and poly(acrylic acid) brushes.34-38 These annealed polyelectrolyte brushes were synthesized by the grafting-from method using self-assembled monolayers of an azo initiator and free radical chain polymerization. Dense brushes with short and long (Mn ≈ 106 g/mol) chains were obtained, but some of them had quite a high polydispersity (Mw/Mn ≈ 2). The scaling laws were also confirmed for poly(styrene sodium sulfonate) (PSS) brushes. The quenched polyelectrolyte brushes were prepared by the grafting to procedure. Polystyrene chains were first grafted to the surface. In the second step, the neutral polystyrene chains were sulfonated in situ to obtain quenched polyelectrolyte chains. Both planar5,6 and colloidal silica4 substrates were successfully grafted with PSS brushes. The swelling behavior of PSS brushlike systems obtained by other methods was also investigated: a PSS shell grown on the surface of latex particles by photoemulsion polymerization39 and PSS layers adsorbed on a solid substrate with a poly(tert-butylstyrene) block as a hydrophobic anchor40 or adsorbed at the liquid-air interface with a poly(ethylethylene) (34) Biesalski, M.; Ru¨he, J. Macromolecules 1999, 32, 2309. (35) Biesalski, M.; Johannsmann, D.; Ru¨he, J. J. Chem. Phys. 1999, 111, 7029. (36) Biesalski, M.; Johannsmann, D.; Ru¨he, J. J. Chem. Phys. 2002, 117, 4988. (37) Biesalski, M.; Ru¨he, J. Macromolecules 2002, 35, 499. (38) Biesalski, M.; Johannsmann, D.; Ru¨he, J. J. Chem. Phys. 2004, 120, 8807. (39) Guo, X.; Ballauff, M. Phys. ReV. E 2001, 64, 051406. (40) Balastre, M.; Li, F.; Schorr, P.; Yang, J.; Mays, J. W.; Tirrell, M. V. Macromolecules 2002, 35, 9480.

pH-ResponsiVe Polybase Brushes

anchor block.41,42 Guenoun’s group studied PSS brushes formed by a block copolymer in spherical geometry as micelles or in planar geometry as Langmuir films.43-45 The scaling behavior of poly(acrylic acid) brushes obtained with a block copolymer in water-dispersed lamellar phases46 and at a liquid-air interface47-48 was not in good agreement with the annealed osmotic brush regime predicted by mean-field scaling theories. Prinz et al. investigated poly(styrene)-b-poly(2-vinylpyridine) diblock copolymers at water-air and solid-water interfaces.49,50 Ryan et al. investigated the responsive properties of poly(2(diethylamino)ethyl methacrylate)) brushes in which chains were covalently attached to a solid substrate.19 To our knowledge, only one publication has been devoted to the structure of poly(2-(dimethylamino)ethyl methacrylate)) (PDMAEMA) brushes. The brushes were obtained by the adsorption of a copolymer containing 70% DMAEMA on hydrophobic surfaces.51 However, the results were not compared with any scaling model. In this article, we report on the synthesis and the swelling behavior of poly(2-(dimethylamino)ethyl methacrylate)) (PDMAEMA) surface-attached chains. These polybase brushes were obtained by preparing a self-assembled monolayer of an initiator and growing polymer chains by Atom Transfer Radical Polymerization. The surface-initiated controlled radical polymerization aims at the formation of dense polymer brushes with low polydispersity. Besides their biocompatible properties, PDMAEMA chains hold some advantages for academic investigations. PDMAEMA brushes can be considered to be neutral polymer brushes in organic solvents and are pH-responsive weak polybase brushes in water. However, quaternization leads to the formation of strong polyelectrolyte brushes. The swelling behavior of poly(2-(dimethylamino)ethyl methacrylate)) (PDMAEMA) and poly(2-(trimethylamino)ethyl methacrylate)) (PTMAEMA) brushes is then investigated using reflectivity techniques such as ellipsometry and neutron specular reflection. The data obtained with PDMAEMA brushes in methanol and PTMAEMA brushes in water with and without salt are compared to theoretical predictions. From the data obtained with PDMAEMA brushes at various pH values, the effective charge ratio of the polybase brush is determined as a function of pH by using scaling laws. Experimental Section Materials. 2-(Dimethylamino)ethyl methacrylate (Aldrich, 98%), triethylamine (Aldrich, 99.5%), and solvents such as dimethylformamide (SDS, 99%) and tetrahydrofuran (SDS, 95%) were passed through a column of activated basic alumina and degassed with high-purity nitrogen prior to use. Dimethylchlorosilane (Roth Sochiel, 98%), chlorododecyldimethylsilane (Aldrich, 95%), 10-undecen1-ol (Aldrich, 98%), 2-bromoisobutyryl bromide (Aldrich, 98%), 1,1,4,7,10,10-hexamethyltriethylene tetramine (Aldrich, 97%), ethyl2-bromoisobutyrate (Aldrich, 98%), anhydrous tetrahydrofuran (Aldrich, 99.9%), and anhydrous toluene (Aldrich, 99.8%) were used as received. (41) Ahrens, H.; Fo¨rster, S.; Helm, C. A. Macromolecules 1997, 30, 8447. (42) Ahrens, H.; Fo¨rster, S.; Helm, C. A. Phys. ReV. Lett. 1998, 81, 4172. (43) Guenoun, P.; Muller, F.; Delsanti, M.; Auvray, L.; Chen, Y. J.; Mays, J. W.; Tirrell, M. Phys. ReV. Lett. 1998, 81, 3872. (44) Romet-Lemonne, G.; Daillant, J.; Guenoun, P.; Yang, J.; Mays, J. W. Phys. ReV. Lett. 2004, 93, 148301. (45) Muller, F.; Romet-Lemonne, G.; Delsanti, M.; Mays, J.; Daillant, J.; Guenoun, P. J. Phys.: Condens. Matter 2005, 17, S3355. (46) Bendejacq, D.; Ponsinet, V.; Joanicot, M. Eur. Phys. J. E 2004, 13, 3. (47) Currie, E. P. K.; Sieval, A. B.; Avena, M.; Zuilhof, H.; Sudho¨lter, J. R.; Cohen Stuart, M. A. Langmuir 1999, 15, 7116. (48) Currie, E. P. K.; Sieval, A. B., Fleer, G. J.; Cohen Stuart, M. A. Langmuir 2000, 16, 8324. (49) Prinz, C.; Muller, P.; Maaloum, M. Langmuir 2000, 16, 6636. (50) Prinz, C.; Muller, P.; Maaloum, M. Macromolecules 2000, 33, 4896. (51) An, S. W.; Thirtle, P. N.; Thomas, R. K., Baines, F. L.; Billingham, N. C.; Armes, S. P.; Penfold, J. Macromolecules 1999, 32, 2731.

Langmuir, Vol. 23, No. 10, 2007 5771 Substrates are polished 〈100〉 silicon wafers (from ACM) with various geometric shapes. Trapezoidal crystals (70 × 10 × 1.5 mm3 with an angle of 45°) were used for FTIR-ATR spectroscopy measurements, (100 × 50 × 10 mm3) blocks were used for neutron reflectivity experiments, and standard wafers of 2 in. diameter were used for in situ ellipsometry experiments. Silicon substrates were cleaned by treatment with freshly prepared piranha solution (70:30 v/v concentrated H2SO4/30% aqueous H2O2) at 150 °C for 30 min. The substrates were then rinsed with pure water (Millipore, resistivity ) 18.2 MΩ·cm), cleaned by ultrasonication in water for 1 min, and dried under nitrogen. Initiator Synthesis and Monolayer Self-Assembly. 10-Undecen1-yl-2-bromo-2-methylpropionate. A solution of 4.262 g (25 mmol) of 10-undecen-1-ol in 25 mL of dry tetrahydrofuran was first prepared. Triethylamine (4.5 mL, 30 mmol) was then added, followed by drop addition of 3.5 mL (28.3 mmol) of 2-bromoisobutyryl bromide in 10 mL of dry tetrahydrofuran. The mixture was stirred at room temperature for 24 h, diluted in 50 mL of hexane, and washed with 2 mol/L HCl and twice with water. The organic phase was dried with magnesium sulfate and filtered. The solvent was removed from the filtrate under reduced pressure, and the colorless, oily residue was purified by flash column chromatography (90:10 v/v petroleum ether/ethyl acetate). The retention factor Rf, which is the ratio of the distance covered by the compound front to that covered by the solvent, was equal to 0.65. The ester colorless solution was concentrated with a rotavap and dried under vacuum overnight. The free initiator can be stored under nitrogen at 10 °C. (11-2-(2-Bromo-2-methyl)propionyloxy)undecyldimethylchlorosilane. To a dry flask were added 0.704 g (2.21 mmol) of 10-undecen-1-yl 2-bromo-2-methylpropionate and 2.2 mL (22.31 mmol) of dimethylchlorosilane, followed by the addition of Karstedt catalyst (20 µL, 500 ppm Pt equiv). The mixture was stirred at room temperature under an atmosphere of nitrogen overnight in the dark. The solution was quickly filtered through a plug of silica gel to remove the catalyst, and the excess reagent was removed under vacuum. The silane initiator was freshly prepared prior to use. Initiator Monolayer Self-Assembly. Freshly cleaned silicon substrates were placed into a dried reactor flushed with high-purity nitrogen for 30 min. A solution of 50 µL of (11-2-(2-bromo-2methyl)propionyloxy)undecyldimethylchlorosilane in 10 mL of anhydrous toluene was added to the reactor. The silicon crystals were left in the solution for 2 h under an atmosphere of nitrogen. They were then removed, rinsed with toluene, cleaned by ultrasonication in toluene for 1 min, and dried in a nitrogen stream. Chlorododecyldimethylsilane was also used for the formation of self-assembled monolayers. A mixture of (11-2-(2-bromo-2-methyl)propionyloxy)undecyldimethylchlorosilane and chlorododecyldimethylsilane in dry toluene allowed us to prepare mixed monolayers of initiator and the alkyl compound. Mixed monolayers were obtained at different ratios in order to generate polymer brushes of various grafting densities. Surface-Initiated Atom Transfer Radical Polymerization. The reactor containing the functionalized silicon substrate was removed, back-filled with nitrogen three times, and left under a nitrogen atmosphere. The polymerization of 2-(dimethylamino)ethyl methacrylate with the surface-attached initiator was performed at a concentration of 60% w/w in a stoichiometric mixture of DMF and THF. A first flask containing 54.75 mg (0.382 mmol) of CuBr was also submitted to this three-time series of evacuation/nitrogen. In a second flask, 248 mg (1.27 mmol) of ethyl-2-bromoisobutyrate free initiator was diluted in 10 mL of dry toluene, and the solution was deoxygenated by bubbling nitrogen for 15 min. In a third flask, a mixture of 10 g (63.6 mmol) of monomer, 0.176 g (0.763 mmol) of HMTETA, and 3.4 g of each solvent was degassed with nitrogen before being added to CuBr. The solution was then transferred to the reactor containing the surface-attached initiator, followed by the addition of 1 mL of solution of the free initiator. All of these transfer processes were performed under a nitrogen atmosphere by using a syringe or a cannula. The polymerization was allowed to proceed at 60 °C for 4 h. The silicon substrates were then removed and rinsed extensively with THF. They were also sonicated in THF for 5 min

5772 Langmuir, Vol. 23, No. 10, 2007 and dried under a nitrogen stream. For in situ measurements in water, the brushes were dried under vacuum to remove traces of organic solvent. Free chains from the polymerization solution were precipitated in cold heptane or petroleum ether and filtered on Bu¨chner funnel. The precipitated compounds were then dried under vacuum. The product was then solubilized in THF and passed through a column of activated basic alumina in order to remove traces of the catalytic complex. It was finally precipitated and dried overnight. In Situ Quaternization. The quaternization of PDMAEMA brushes was carried out with 1.12 M methyl iodide in ethanol at 60 °C for 24 h. After quaternization, the samples were carefully rinsed with ethanol and dried in a nitrogen stream. The quaternized brushes were dried under vacuum to remove traces of ethanol before in situ studies in water were carried out. For the quaternization of PDMAEMA free chains, the above procedure was duplicated. The resulting polymer was precipitated in THF and dried under vacuum overnight. Ellipsometry. The dry and swollen thicknesses of the brushes were determined by ellipsometry. The measurements were performed using a Sentech SE 400 apparatus. The light source was a heliumneon laser (λ ) 632.8 nm), and the angle of incidence was set to 70°. A multilayer model for a flat film was used for the calculation of the thickness of silica, initiator, and grafted polymer layers from experimentally measured ellipsometric angles Ψ and ∆. The refractive indices used for the calculations were n ) 1.460 for the native silica layer, n ) 1.508 for the initiator layer, and n ) 1.517 for the PDMAEMA dry brush. From the dry brush thickness γ(Å), we calculated the grafting density σ(nm-2) as explained in the next section. In situ measurements were performed using a liquid cell with thin glass walls fixed perpendicularly to the light path. Both the refractive index and thickness of the swollen polymer layer were extracted from the ellipsometry data fit. Neutron Reflectivity. Neutron reflectivity measurements were performed at the silicon-liquid interface on the EROS reflectometer at the Laboratoire Le´on Brillouin, CEA-Saclay, France. The experimental procedure and setup were described in detail in previous papers.5,52 Let us state that neutron reflectivity measurements were performed with protonated polymer brushes and deuterated solvents in order to determine the monomer density profile of the brushes. Neutron reflectivity is sensitive to the scattering length density profile perpendicular to the interface F(z). A reliable modelindependent method was chosen to determine F(z). The brush was modeled as a set of layers, each characterized by a fixed thickness and a scattering length density. Two adjacent layers are connected using error functions53 of fixed width to get a continuous profile. The procedure consists of choosing a scattering length density profile and finding the corresponding parameters for which the calculated reflectivity curve best fits the experimental reflectivity data. This reliable method allows the determination of a continuous scattering length density profile without making any assumption about its analytical form. The monomer volume fraction profile φ(z) is then deduced from F(z). γ ) ∫0∞ φ(z) dz is an important parameter because it is independent of the shape of φ(z) and corresponds to the thickness of the dry layer. The thickness of the swollen brush, L, is determined by computing the normalized first moment of the monomer density profile. The dry γ(Å) and swollen L(Å) thicknesses should be the same when they are measured by other techniques. The values of γ and L are then systematically compared to the values measured by ellipsometry. Other Characterization Methods. FTIR-ATR spectra were recorded using a Magna IR 550 (Nicolet) apparatus with an MCT detector cooled with liquid nitrogen. The spectra were recorded with a resolution of 2 cm-1 and a 256-scan accumulation. (52) Tran, Y.; Perrin, P.; Deroo, S.; Lafuma, F. Langmuir 2006, 22, 7543. (53) The scattering-length density profile is given by F(z) ) ∑i((Fi - Fi+1)/ (2))(1 - erf (z - zi)/(wi)) where the layer i of thickness (zi - zi+1) is associated with the fixed coherent scattering-length density Fi and the transition between layers i and i + 1 is described using error functions of fixed width wi.

Sanjuan et al. Scheme 1. Synthesis of Attachable Initiator 11-(2-Bromo-2-methyl)propionyloxyundecenyldimethylchlorosilane

1RMN spectra were recorded on a 400 MHz Bruker apparatus. The solvents used were deuterated toluene for the initiator, deuterated chloroform for PDMAEMA neutral polymer, and deuterium oxide for PTMAEMA polyelectrolyte. Acid/base titration was performed with a commercial apparatus (Titrando 809/Metrohm) using a 0.1 mol/L NaOH solution.

Results and Discussion Synthesis of PDMAEMA and PTMAEMA Brushes. The synthesis of the surface-attachable initiator followed the same strategy used by Husseman et al.11 and Matyjaszewski et al.12 It is illustrated in Scheme 1, and the experimental conditions are described in detail in the Experimental Section. (11-2-(2-Bromo2-methyl)propionyloxy)undecyldimethylchlorosilane was obtained after the esterification of 10-undecen-1-ol with 2-bromoisobutyryl bromide and hydrosilylation with dimethylchlorosilane. This compound contains chlorosilane reactive species that are able to bond to silica surfaces and a latent R-halo ester that can be used to initiate the ATRP of methacrylate monomers. The 1H NMR spectrum of the attachable initiator is displayed in Figure 1A. The spectrum shows the presence of methyl protons for the groups adjacent to the bromine with peak 1. It also shows the absence of any unsaturated hydrocarbon above 5 ppm and the presence of methyl protons adjacent to the chlorosilane group with peaks 4 and 5, indicating that the esterification and hydrosilylation reactions were effective. The initiator was covalently attached to the silica surface by a self-assembling technique. The use of monofunctional silane compounds (instead of trifunctional) prevented any cross-linking of the initiator molecules and allowed the formation of welldefined initiator monolayers. Initiator molecules, which were only physically and not covalently linked to the surface, could be readily removed by solvent. This strategy also ensured that homogeneous mixed monolayers of the ATRP initiator and the alkyl compound were obtained. The use of mixed monolayers allows the synthesis of polymer brushes of the same chain length and various grafting densities. The chemical identity of the selfassembled monolayer was proven by FTIR-ATR measurements. In Figure 1B, the FTIR-ATR spectrum shows typical vibrational bands of the self-assembled monolayer that arise from the symmetric and the asymmetric stretching vibrations of -CH2groups at 2852 and 2925 cm-1 and the asymmetric stretching vibrations of -CH3 groups at 2962 cm-1. The FTIR-ATR technique did not allow the determination of the ratio of the initiator compound in mixed monolayers. The intensities of typical vibrational bands that differentiate the initiator from the attachable alkyl compound such as for -CH3 (at 2962 cm-1) and -CdO (at 1730 cm-1) groups were too weak to be analyzed quanti-

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Scheme 2. Chemical Diagram Describing the Synthesis of Poly(2-(dimethylamino)ethyl Methacrylate) (PDMAEMA) and Poly(2-(trimethylamino)ethyl Methacrylate) (PTMAEMA) Brushes Using Surface-Initiated Atom Transfer Radical Polymerization (ATRP)a

Figure 1. (A) 1H RMN spectrum in deuterated toluene and chemical formula of (11-2-(2-bromo-2-methyl)propionyloxy)undecyldimethylchlorosilane. (B) FTIR spectrum in attenuated total reflection of the self-assembled initiator monolayer.

a First, the initiator was covalently grafted onto silicon substrates in a self-assembled monolayer. Then, the PDMAEMA polymer was grown in situ by ATRP from the surface-attached initiator. The PDMAEMA weak polyelectrolyte was then quaternized to obtain the PTMAEMA strong polyelectrolyte.

tatively. The ratio of the initiator in mixed monolayers could not be measured by ellipsometry because the thickness of initiator monolayers is comparable to the thickness of alkyl monolayers. Chlorododecyldimethylsilane was actually chosen because its length is close to the length of the attachable initiator. However, our purpose was not to give a detailed characterization of the mixed monolayers. The strategy of formation of mixed monolayers was essentially employed in order to generate polymer brushes with various grafting densities. It will be shown subsequently that we can readily determine the grafting density of polymer brushes. After the formation of the self-assembled initiator monolayer, the PDMAEMA brush was generated by the atom transfer radical polymerization of the 2-(dimethylamino)ethyl methacrylate monomer using surface-attached initiator. The detailed experimental conditions of the ATRP reaction are described in the Experimental Section. The polymerization was performed in a THF/DMF mixed solution at a fixed monomer concentration (60% w/w monomer) and a fixed reaction time (4 h) in order to

form chains of a fixed molecular mass. The catalyst system was CuBr/HMTETA, and free initiator ethyl-2-bromoisobutyrate was added to the polymerization in a molar-to-initiator ratio of 500. Actually, it has been shown that free initiator was required to provide an overall concentration of ester in the polymerization mixture, which controls the chain growth of both the surfaceattached and bulk initiators.11,13-17 The bulk polymer chains could be separated from the chains covalently bound to the surface by washing with solvent. They were then recovered by precipitation and characterized by size exclusion chromatography (SEC) and 1H NMR spectroscopy. It has also been shown that the grafted polymer chains could be cleaved and recovered. The molecular weights of cleaved and bulk chains were equal, and the polydispersity of cleaved chains was weaker than the polydispersity of bulk chains.11 In our case, we assumed that the size and the polydispersity of grafted and bulk polymer chains were the same. All PDMAEMA brushes were generated under the same polymerization conditions (monomer concentration, monomer-to-initiator ratio, reaction time, and reaction temperature) in order to have the same chain length. The molecular weight, Mn, and the polydispersity of the chains determined by SEC measurements were 43 000 g/mol and 1.35, respectively. The grafting density, which corresponds to the number of chains per unit area, was set by the ratio of initiators in the self-assembled monolayer. It was determined from the dry thickness of the brush measured by ellipsometry. The grafting density was calculated from the dry thickness γ(Å) and the molecular weight Mn by

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σ)

γdNA Mn

Sanjuan et al.

(5)

where d is the density (d ) 1.318 g/cm3 for PDMAEMA) and NA is Avogadro’s number. A frequently used parameter is also the distance between two grafting sites D, which is given by D ) (1)/(σ1/2). PDMAEMA brushes with grafting densities from 0.1 to 0.5 nm-2 were synthesized. It is worth noticing that brushes with a packing density of σ ) 0.5 nm-2 (or D ) 14.2 Å) are very difficult to obtain (it may not be possible) using the grafting to method with such long polymer chains (Mn ) 40 000 g/mol). The quaternization reaction of the PDMAEMA brush was performed with methyl iodide in ethanol to obtain a brush of positively charged PTMAEMA chains. Because the reaction proceeded very slowly at room temperature, a complete quaternization reaction could be expected after 24 h using a temperature of 60 °C. The quaternization reaction was carried out under these mild conditions to avoid chain degrafting. An analogous procedure was duplicated for free chains to obtain PTMAEMA molecules, which could be analyzed by 1H NMR and FTIR spectroscopy. Figure 2A shows 1H NMR spectra of PDMAEMA and PTMAEMA polymers. The displacement of peaks 4 and 5 is characteristic of the conversion of tertiary amine group to quaternary amine group. Quantitative analysis showed that the quaternization reaction was complete if peaks 4 and 5 were compared to peak 1 relative to the methyl protons adjacent to the carboxyl group. This result was also in good agreement with titration measurements. Figure 2B displays FTIR-ATR spectra of the PDMAEMA brush and the PTMAEMA brush after quaternization. The same infrared spectra were obtained with PDMAEMA and PTMAEMA free chains by transmission. The disappearance of the absorption bands at 2769 and 2820 cm-1, which are attributed to symmetric stretching vibrations of -CH3 of the tertiary amine groups, proved that the quaternization reaction of the polymer brush was complete. The appearance of the broad band between 3700 and 3200 cm-1 is characteristic of the presence of OH groups as a result of the formation of a hydrophilic polyelectrolyte. The characteristic peak at 1729 cm-1 for the CdO stretching vibration allowed the determination of the degrafting rate. The equal intensity of this band when comparing the spectra of PDMAEMA and PTMAEMA brushes clearly showed that the quaternization reaction was performed under mild conditions because all polymer chains remained attached to the surface. The complete conversion into PTMAEMA strong polyelectrolyte brushes without any chain degrafting was observed for all samples investigated with grafting densities varying from 0.1 to 0.5 nm-2. Scaling Laws of Neutral Polymer and Polyelectrolyte Brushes. The swelling behavior of PDMAEMA and PTMAEMA brushes was investigated in detail using ellipsometry. The neutral polymer and the strong polyelectrolyte brushes were immersed in good solvents, PDMAEMA in methanol and PTMAEMA in water. In situ ellipsometric measurements with a liquid cell were performed to determine the thickness of the swollen layer L(Å). The degree of swelling defined as the ratio of the thickness of the swollen brush to that of the dry brush, L/γ, gives the stretching of the chains in the solvent directly. Figure 3 displays the degree of swelling of PDMAEMA brushes in methanol and PTMAEMA brushes in water as a function of the grafting density. The grafting density of the brushes was deduced from the dry thickness of PDMAEMA brushes. The values were valid for both PDMAEMA and PTMAEMA brushes because FTIR-ATR spectra proved that the quaternization reaction was performed without any chain degrafting. Figure 3 clearly

Figure 2. (A) 1H NMR spectra and chemical formulas of PDMAEMA and PTMAEMA polymers. PDMAEMA was in deuterated chloroform, and PTMAEMA was in deuterated oxide. (B) FTIR spectra in attenuated total reflection of PDMAEMA and PTMAEMA brushes.

shows the decrease in the degree of swelling with the grafting density. It is also obvious that the degree of swelling of polyelectrolyte brushes is greater than that of neutral polymer brushes irrespective of the grafting density. However, at high grafting densities, the swelling of neutral polymer and polyelectrolyte chains is nearly similar whereas at low grafting densities the swelling of charged brushes is almost twice as large as that of neutral brushes. For very dense brushes, the excluded volume effect (responsible for the swelling of neutral polymer

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L ∝ N0σ-2/3 γ

Figure 3. Degree of swelling of the PDMAEMA brushes in methanol (9) and PTMAEMA brushes in water (b) as a function of the grafting density. The degree of swelling is the ratio between the thickness of the swollen and dry brushes (L/γ).

Figure 4. Degree of swelling of the PDMAEMA brushes in methanol as a function of the grafting density. The degree of swelling is the ratio between the thickness of the swollen and dry brushes (L/γ). The data for PDMAEMA brushes (b) are compared with the data obtained with poly(4-vinylpyridine) brushes (O) taken from Biesalski et al.37

brushes) becomes as strong as the electrostatic effect (responsible for the swelling of polyelectrolyte brushes). The osmotic pressure of monomers in neutral polymer brushes becomes as high as the osmotic pressure of counterions in polyelectrolyte brushes. The data can be fitted with power laws that are in good agreement with scaling mean-field models as shown in detail in the following text. Figure 4 shows the logarithmic plot of the degree of swelling of the PDMAEMA brush in methanol as a function of the grafting density. Our data, represented by filled circles, were compared to the results reported by Biesalski et al.,37 who studied poly(4-vinylpyridine) (PVP) brushes. The best data fit gives a power law with an exponent of -0.70, in good agreement with the value of -2/3 predicted by theoretical scaling laws. Actually, if a dry layer contains only polymer chains, because the volume, V, occupied by a single chain is given by V ) Na3 ) γ × D2, then the dry thickness, γ, and the grafting density, σ, can be linked by the relation

γ ) Na3σ

(6)

The scaling relation for a neutral polymer brush under good solvent conditions is given by L ∝ Na5/3σ1/3. The degree of swelling L/γ is then independent of the chain length and follows a power law dependence of the grafting density with an exponent of -2/3

(7)

Accordingly, data from brushes of different chain lengths can be compared in the same plot. It should also be mentioned that eq 7 is strictly valid if the ratio of the monomer size in the swollen brush to that in the dry brush is independent of the grafting density of the brushes. This condition was likely to be relevant for the brushes investigated. Actually, the range of investigated grafting densities was such that polymer chains were not obstructed as a result of swelling because the shortest distance between two anchoring points (D ) 14.2 Å) was larger than the size of a monomer (a ) 5.8 Å calculated from the density). In addition, it should be noted that our results for PDMAEMA brushes are in good agreement with those of Biesalski et al.37 In both cases, a -0.7 exponent was found, which points out that the swelling behavior was the same for both brushes. Moreover, it also shows that the ratio between the size of the monomer in the swollen and dry brushes is the same for PDMAEMA and PVP brushes in methanol. Figure 5 shows the degree of swelling of PTMAEMA brushes in water as a function of the grafting density. Again, the data were represented by filled circles and were compared with the data reported by Biesalski et al.37 on poly(N-methyl-4-vinylpyridinium iodide) (MePVP) brushes. For these polyelectrolyte brushes, the best data fit gives a power law with an exponent of -0.95. It is in good agreement with theoretical expectations of a scaling exponent of -1. The scaling laws predict that the swollen thickness of a polyelectrolyte brush in the osmotic regime depends on the chain length N and the degree of dissociation f but not on the grafting density as given by eq 2: L ∝ Naf1/2. The degree of swelling for polyelectrolyte brushes calculated from eqs 2 and 6 is independent of the chain length and is a power law of the grafting density with an exponent of -1

L ∝ N0σ-1f1/2 γ

(8)

Equation 8 describes the swelling behavior of brushes with different chain lengths within the valid range of grafting density. It should be particularly pointed out that the ratio between the monomer size in water and in the dry free-solvent state is the same for PTMAEMA and MePVP brushes following the scaling laws. The swelling behavior that was found to be the same for PDMAEMA and PVP neutral polymer brushes is again similar for PTMAEMA and MePVP charged polymer brushes. It should be highlighted that the combination of our results and the results of Biesalski et al. allowed the scaling analysis of polymer brushes on four decades of grafting densities. PDMAEMA brushes prepared with atom transfer radical polymerization are dense brushes that are not accessible with free radical procedures. However, PVP brushes synthesized by Biesalski et al. with free radical polymerization have longer chains that are not attainable by ATRP. Both chemical methods yield complementary molecular characteristics of the brushes (chain length and grafting density). Figure 6 shows the variation in the swollen thickness of the PTMAEMA brush as a function of the concentration of NaCl added salt. The data are given for two grafting densities: σ ) 0.230 and 0.123 nm-2 (Figure 6A,B, respectively). For both grafting densities, two regimes can be distinguished. At low salt concentrations, the thickness is independent of the salt concentration, whereas at high salt concentrations, the data are fitted with a power law with an exponent of -0.33 ( 0.01. These experimental results are in good agreement with theoretical

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Figure 5. Degree of swelling of the PTMAEMA brushes in water as a function of the grafting density. The degree of swelling is the ratio between the thickness of the swollen and dry brushes (L/γ). The data for PTMAEMA brushes (b) are compared with the data obtained with poly(N-methyl-4-vinylpyridinium iodide) brushes (O) taken from Biesalski et al.37

Figure 6. Swollen thickness of the PTMAEMA brush as a function of NaCl concentration. The data are shown for brushes with grafting densities of σ ) 0.230 (A) and 0.123 nm-2 (B). The crossover NaCl concentrations between the osmotic and salted-brush regimes are 1.30 and 0.70 mol/L for σ ) 0.230 and 0.123 nm-2, respectively.

predictions. The first regime corresponds to the osmotic brush regime. In this regime, the quenched polyelectrolyte brush is not sensitive to the added electrolytes, and the brush is simply stretched by the osmotic pressure of the counterions trapped inside the brush. In the salted-brush regime, the brush thickness is expected to follow a power law dependence with salt concentration with an exponent of -1/3. This scaling behavior of polyelectrolyte brushes as a function of added salt has been found experimentally for both quenched and annealed poly-

Sanjuan et al.

Figure 7. Neutron reflectivity curves of the PDMAEMA brush (σ ) 0.230 nm-2) at various pH values: 2, 7, and pH 10. The corresponding volume fraction profiles that best fit the experimental data are shown in Figure 8.

electrolytes. For instance, such behavior was found for poly(sodium styrene sulfonate)4-5,39-45 and poly(N-methyl-4vinylpyridinium iodide)38 brushes as well as for poly(methacrylic acid)36 and poly(acrylic acid)46 brushes. From a theoretical point of view, the crossover concentration between the regimes of the osmotic brush and the salted brush is expected to correspond to the concentration of counterions inside the brush. According to our experimental measurements, the crossover concentrations are 1.30 and 0.70 mol/L for brushes with grafting densities of 0.230 and 0.123 nm-2, respectively. They matched the values of the internal concentration of counterions in view of the so-called Manning-Oosawa theory of counterion condensation.54,55 Actually, the concentration of chemically charged monomers of the brush can be calculated for each grafting density. Brushes with σ ) 0.230 and 0.123 nm-2 have volume concentrations of 2.92 and 1.55 mol/L, respectively. According to the theoretical predictions, the ratio between the crossover concentration and the concentration of charged monomers should be of the order of the effective charge fraction following Manning counterion condensation.54,55 For both grafting densities, a value of about 0.44 was calculated for the effective charge fraction. It has been shown by osmotic pressure measurements and by cryoscopy that sulfonate polyelectrolytes such as poly(sodium styrene sulfonate) (PSS) and poly(sodium2-acrylamide-2-methyl propane sulfonate) (AMPS) have an effective charge of 0.36 for a chemical charge of 1.56 The same value has also been found for PSS at the liquid-air interface in Langmuir films using scaling laws for polyelectrolyte brushes.43 Dependence of Weak Polyelectrolyte Brushes on pH. The swelling behavior of PDMAEMA brushes as a function of pH was investigated using ellipsometry and neutron reflectivity. The brushes were immersed in aqueous solutions at various pH values. Figure 7 shows typical neutron reflectivity curves of PDMAEMA brushes at pH 2, 7, and 10. The reflectivity curve displays more marked Kiessig fringes with a larger spacing as the pH increases. This seems to indicate that the brush is less extended with a more abrupt profile as the pH of the solution becomes more basic, as shown in the corresponding volume fraction profiles that best fit these reflectivity data. In Figure 8A, the density profiles of PDMAEMA brushes are given at pH 2, 7, and 10 and in methanol. The profile of the dry (54) Manning, G. S. J. Chem. Phys. 1969, 51, 924. (55) Oosawa F. Polyelectrolytes; Marcel Dekker: New York, 1971. (56) Essafi, W.; Lafuma, F.; Baigl, D.; Williams, C. E. Europhys. Lett. 2005, 71, 938.

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Figure 8. (A) Monomer volume fraction profiles of the PDMAEMA brush at different pH values. The density profiles of the PDMAEMA brush in methanol and the dry brush are also given. (B) Fits of the density profile of the PDMAEMA brush at pH 2 and in methanol by Gaussian and parabolic functions, respectively. The fits are represented by solid lines, and the “layered” profiles are represented by dashed lines.

brush is given as an indication to illustrate that its integral corresponds to the dry thickness γ ) ∫0∞ φ(z) dz. It appears that the PDMAEMA brush is less extended in methanol than in water irrespective of pH. It is also clear that the brush is more stretched as the pH decreases. The shape of the profiles was analyzed in detail by fitting the profiles with a parabolic or Gaussian function (Figure 8B). The profile of a PDMAEMA brush in methanol could be well adjusted by a parabolic function, as expected for a neutral polymer brush in a good solvent.57 Self-consistent field computations also showed a Gaussian profile58 for the polyelectrolyte brush in the osmotic regime. The profile of the PDMAEMA brush at pH 2 and 7 (fit not shown) could be well adjusted by a Gaussian function. In contrast, the profile at pH 10 could not be fitted by a Gaussian profile. The swollen thickness of the brush was determined by computing the normalized first moment of the “layered” profile. The neutron reflectivity data were compared to the ellipsometry data. Figure 9 gives the swollen thickness of the PDMAEMA brush as a function of pH. The data were obtained for PDMAEMA brushes with different grafting densities: σ ) 0.230 nm-2 (γ ) 130 Å), σ ) 0.153 nm-2 (γ ) 90 Å), and σ ) 0.123 nm-2 (γ ) 58 Å). The thicknesses of a PDMAEMA brush in methanol, a PTMAEMA brush in water, and a dry PDMAEMA brush are also shown in the graphs. Note that only the brush with σ ) 0.230 nm-2 was measured by both neutron reflectivity and ellipsometry, which provide similar results. In addition, there was no hysteresis effect with the pH, proving that the brush (57) Parabolic functions: φ(z) ) φ0 (1 - (z2/h2)). (58) Gaussian functions: φ(z) ) φ0 exp(- (z2/h2)).

Figure 9. Swollen thickness of the PDMAEMA brush as a function of pH, measured by ellipsometry (b) and neutron reflectivity (O). The swollen thicknesses of the PDMAEMA brush in methanol and the PTMAEMA brush in water are also shown. The dry thickness of the PDMAEMA brush is given as a reference.

swelling was completely reversible. For all investigated samples, the swollen thickness of the PDMAEMA brush is larger than the thickness of the PDMAEMA brush in methanol and lower than the thickness of the PTMAEMA brush in water. As expected, these results suggest that the swelling behavior of the pHresponsive brush is intermediate between that of a neutral polymer in a good solvent and a quenched polyelectrolyte brush in the osmotic regime. It was also observed that the upper limit of the swollen thickness (PTMAEMA brush in water) was reached only for pH values lower than 3. Actually, the complete ionization of PDMAEMA should be expected at less acidic pH. The slight difference between the values of the PTMAEMA brush thickness in water might be surprising when following the scaling laws. Identical values should be expected for brushes of different grafting density but the same chain length. Actually, this is due to the slight discrepancy in the molecular weight of the samples investigated.

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Sanjuan et al.

between the osmotic pressures of the counterions and the monomers is then given by π/π0 ) 2f(L02)/(Lγ). We calculated the effective charge ratio f and the ratio of the osmotic pressures π/π0 at each pH. We considered that the calculation of f is valid provided that π/π0 is higher than 1. The evolution of the effective charge ratio with pH is quite similar for the three grafting densities investigated. It suggests that the ionization of PDMAEMA attached chains or the proportion of H+ cations is the same inside the brush irrespective of the grafting density. In the investigated range of grafting densities, the distance between two anchoring points, from D ) 14-29 Å, is much greater than the size of the H+ cation and is not slight enough to perturb the exchange of ions between the inside and the outside of the brush. Figure 10. Effective charge ratio of PDMAEMA brushes as a function of pH. The effective charge ratio, f, is calculated using the scaling law for the polyelectrolyte brush in the osmotic regime. The determination of f is valid provided that the osmotic pressure of the counterions, π, is higher than that of the monomers in the neutral polymer brush, π0. The data were obtained with PDMAEMA brushes of different grafting densities: σ ) 0.230 (b), 0.152 (2), and 0.123 nm-2 (9).

In Figure 10, the effective charge ratio of PDMAEMA brushes is plotted as a function of pH. Using the scaling law of the osmotic brush (eq 2), we calculated the effective charge ratio f ) f+((L)/(L+))2 where L is the pH-dependent thickness and L+ and f+ are the thickness and the effective charge ratio of the PTMAEMA brush in water, respectively. f+ is equal to 0.44 as determined above. However, the determination of f is valid only for the polyelectrolyte brush in the osmotic regime. Accordingly, the osmotic pressure of the counterions in the polyelectrolyte brush must be at least higher than the osmotic pressure of monomers in the neutral polymer brush. For a polyelectrolyte brush, the osmotic pressure of the counterions is given by

π ) kT f

Nσ L

(9)

For a neutral polymer brush, the osmotic pressure of the monomers is

( )

Nσ 1 π0 ) kTV 2 L0

2

(10)

where V is the excluded volume and L0 is the thickness of the uncharged brush. L0 is taken at pH 10 where PDMAEMA chains are not protonated. V is assumed to be equal to a3 to maximize the value of the osmotic pressure of the monomers. The ratio

Conclusions We investigated poly(2-(dimethylamino)ethyl methacrylate)) (PDMAEMA) brushes in which the chains are covalently attached to the surface of a solid substrate. PDMAEMA brushes were synthesized using the grafting from method by preparing a selfassembled monolayer of the initiator and growing polymer chains by atom transfer radical polymerization. The surface-initiated controlled radical polymerization allowed the formation of PDMAEMA brushes with weak polydispersity. We showed that PDMAEMA brushes held some advantages for academic investigations. They could be considered to be either neutral brushes or pH-responsive polybase brushes. They could also be studied as strong polyelectrolyte brushes once quaternized to get a permanent charge irrespective of pH. Accordingly, the use of PDMAEMA chains allowed us to perform a whole experimental investigation of various brush types. In all cases, the swelling behavior of the brushes was found to be in good agreement with the scaling laws predicted by mean-field theories, including the models of the neutral polymer brush in a good solvent and the polyelectrolyte brush in the osmotic regime. From the data of the swollen thickness, we were able to calculate the effective charge ratio of PDMAEMA brushes as a function of pH. As an extension of this study, it would be interesting to compare the effective charge ratio of the brush to that of bulk chains. As shown in previous studies, the effective charge ratio of PDMAEMA bulk chains can be determined as a function of pH using osmotic pressure measurements and a cryoscopy technique.56 Acknowledgment. We are thankful to Fabrice Cousin and Alain Menelle from Laboratoire Le´on Brillouin, CEA-Saclay, for their help with the neutron reflectivity experiments. LA063450Z